Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

ASecond-Order SpikingSSM for Wearables

Kartikay Agrawal, Abhijeet Vikram, Vedant Sharma, Vaishnavi Nagabhushana, Ayon Borthakur

TL;DR

SHaRe-SSM introduces a fully spike-based second-order state-space model using Harmonic Resonate-and-Fire neurons to enable energy-efficient, long-range sequence modeling on wearables. It integrates a diagonal-Ω dynamical core with parallel-scan computation and a kernel-based spiking regressor to handle up to 50k steps, while eliminating matrix multiplications and major ANN nonlinearities. Empirically, it achieves competitive HAR accuracy and outperforms first-order SSMs on long-range tasks like EigenWorms and PPG-DaLiA, with substantial energy savings (up to ~52x) over ANN-based alternatives. The work highlights the practicality of neuromorphic, spike-based SSMs for edge healthcare analytics and points toward deployment on neuromorphic hardware such as Intel Loihi2.

Abstract

Spiking neural networks have garnered increasing attention due to their energy efficiency, multiplication-free computation, and sparse event-based processing. In parallel, state space models have emerged as scalable alternatives to transformers for long-range sequence modelling by avoiding quadratic dependence on sequence length. We propose SHaRe-SSM (Spiking Harmonic Resonate-and-Fire State Space Model), a second-order spiking SSM for classification and regression on ultra-long sequences. SHaRe-SSM outperforms transformers and first-order SSMs on average while eliminating matrix multiplications, making it highly suitable for resource-constrained applications. To ensure fast computation over tens of thousands of time steps, we leverage a parallel scan formulation of the underlying dynamical system. Furthermore, we introduce a kernel-based spiking regressor, which enables the accurate modelling of dependencies in sequences of up to 50k steps. Our results demonstrate that SHaRe-SSM achieves superior long-range modelling capability with energy efficiency (52.1x less than ANN-based second order SSM), positioning it as a strong candidate for resource-constrained devices such as wearables

ASecond-Order SpikingSSM for Wearables

TL;DR

SHaRe-SSM introduces a fully spike-based second-order state-space model using Harmonic Resonate-and-Fire neurons to enable energy-efficient, long-range sequence modeling on wearables. It integrates a diagonal-Ω dynamical core with parallel-scan computation and a kernel-based spiking regressor to handle up to 50k steps, while eliminating matrix multiplications and major ANN nonlinearities. Empirically, it achieves competitive HAR accuracy and outperforms first-order SSMs on long-range tasks like EigenWorms and PPG-DaLiA, with substantial energy savings (up to ~52x) over ANN-based alternatives. The work highlights the practicality of neuromorphic, spike-based SSMs for edge healthcare analytics and points toward deployment on neuromorphic hardware such as Intel Loihi2.

Abstract

Spiking neural networks have garnered increasing attention due to their energy efficiency, multiplication-free computation, and sparse event-based processing. In parallel, state space models have emerged as scalable alternatives to transformers for long-range sequence modelling by avoiding quadratic dependence on sequence length. We propose SHaRe-SSM (Spiking Harmonic Resonate-and-Fire State Space Model), a second-order spiking SSM for classification and regression on ultra-long sequences. SHaRe-SSM outperforms transformers and first-order SSMs on average while eliminating matrix multiplications, making it highly suitable for resource-constrained applications. To ensure fast computation over tens of thousands of time steps, we leverage a parallel scan formulation of the underlying dynamical system. Furthermore, we introduce a kernel-based spiking regressor, which enables the accurate modelling of dependencies in sequences of up to 50k steps. Our results demonstrate that SHaRe-SSM achieves superior long-range modelling capability with energy efficiency (52.1x less than ANN-based second order SSM), positioning it as a strong candidate for resource-constrained devices such as wearables
Paper Structure (16 sections, 3 theorems, 35 equations, 1 figure, 3 tables, 1 algorithm)

This paper contains 16 sections, 3 theorems, 35 equations, 1 figure, 3 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Methods
  3. Network Description
  4. Encoder and Decoder
  5. Discretisation methods
  6. Emperical Results
  7. Human Activity Recognition
  8. Very-Long Range Interactions
  9. Energy computation
  10. Discussion
  11. Technical Appendix
  12. Background Theory
  13. Implicit discretisation (IM):
  14. Implicit-Explicit discretisation (IMEX):
  15. Parallel scan in SHaRe-SSM
  16. ...and 1 more sections

Key Result

Proposition A.1

Let $M^{\text{IM}} \in \mathbb R^{2p\times 2p}$ be the hidden-to-hidden weight matrix of the implicit model SHaRe-SSM-IM eq:im_model. We assume that $\Omega_{j} \geq 0$ for all diagonal elements $j=1,\dots,p$ of $\Omega$, and further that $\Delta t>0$. Then, the complex eigenvalues of $M^{\text{IM}} with $\lambda_{j_1} = \overline{\lambda_{j_2}}$. Moreover, the spectral radius $\rho(M^{\text{IM}})

Figures (1)

  • Figure 1: Variation of energy computation of a LinOSS Block rusch2025oscillatory to the SHaRe-SSM Block for EigenWorms with respect to State (P), Hidden size (H).

Theorems & Definitions (6)

  • Proposition A.1
  • proof
  • Proposition A.2
  • proof
  • Proposition A.3
  • proof